One, two! One, two! And through and throughThe vorpal blade went snicker-snack!He left it dead, and with its headHe went galumphing back.

becomes

One two, one two, by the medium,The sword vorpal makes stalemate-with-side!The demolished animal, with its head,It returns gallomphant.

Not bad, but "stalemate-with-side" is disappointingly literal.

I imagine that no other poem has been rewritten for satire as many times as "Jabberwocky". (There's a whole page of such poems, though the page incorrectly calls them "parodies".) I first learned of the poem when I was in grade school because of a brilliant satire in MAD magazine, written by veteran Frank Jacobs. Here it is, annotated with inspiration from Martin Gardner's The Annotated Alice:

You've just wound down nineteen straight hours of Nintendo. Your brain is totally waxed, and as you crash you find yourself mumbling incoherently verse after verse of MAD's...

"Beware the Shadow Boss, my son! [final enemy in Double Dragon, who turns out to be your brother, a poor excuse for making game only single-player]The Killer Clams, the Mummy Men! [Karnov; Castlevania]Don't Goombah with a Neul, and shun [mushroom enemies in Super Mario Bros.; Solomon's Key enemy]The Death Breath known as Ken!" [boss in Kid Niki: Radical Ninja,; hero of Street Fighter: 2010]

He Holtzed at Zigmos from afar, [Metroid flying enemy; Hudson's Adventure Island enemy]Dodged Zombie Slime with lightning scroll, [combination of two Dragon Warrior enemies; not sure, but such a scroll appears in Domino's Pizza-licensed game Yo! Noid]While Zelda in her Mamda Jar [Solomon's Key]Made Yuki with a Troll. [evil samurai in Legend of Kage; various, including Joust, Shadowgate]